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2006-Fall-Final_s

# 2006-Fall-Final_s - More PastPaper...

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Unformatted text preview: More PastPaper: http://ihome.ust.hk/~cs_gxx I S M T 1 1 1 F 0 6 F i n a l E x a m Suggested Solution Question 1: (a) 71.5 ± 2.06 × 30.55 / 26 =71.5 ± 12.34 = [59.16, 83.84] (b) With 95% confidence the true mean will be enclosed in the interval. That is, if we take a large number of samples and construct the intervals as in (a) then 95% of the intervals will enclose the true mean. (c) (80.55+59.45)/2=70 (d) (80.55-59.45)/2=10.45. SE=10.55/1.96=5.33 2 2 (1.96) (31.98) 18 ( ) / 36 =0.111 ± 0.103 (e) n ≥ = 61.4 , n = 62 (f) 0.111 ± 1.96 × 2 8 99 Question 2: (a) H 0 : p 2 − p1 = 0 vs H a : p 2 − p1 > 0 (0.5 − 0.44) 0.06 (b) = = 1.087 < 1.645 , accept H 0 . 66 + 90 156 ⎛ 1 1 ⎞ 0.0552 + (1 − )⎜ ⎟ 150 + 180 330 ⎝ 150 180 ⎠ that the economic outlook this year is not better than last year. (c) p-value = 0.1379 0.5 − 0.44 ˆ (d) P{ p 2 > 0.5} = P{Z > } = P{Z > 1.62} = 0.0526 . 0.44(0.56) / 180 Question 3: (a) Sample means have normal distribution with mean 3 and variance 1/ 25 = 0.2, therefore P{2.9 ≤ x ≤ 3.3} = P{−0.5 ≤ z ≤ 1.5} = 0.6247 (b) 0.36 = margin of error 0.36/(0.2)=1.8 = critical value α / 2 = 0.0359 , 1 − α = 0.9282 (c) t-distribution with d.f. 24, because t 0.05 = 1.71 and t 0.1 =1.32 so the answer is 5%. 0.2 − 0.1587 ˆ (d) P{ X > 4} = P{Z > 1} = 0.1587, P{ p > 0.2} = P{Z > } = 0.2943 . 0.1587(1 − 0.1587) / 25 Question 4: (a) -4.28+0.254 × 30=3.34 days (b) (0.254 -0.2)/0.0285=1.895>1.771 reject H 0 . (c) 0.254 ± 2.16(0.0285) (d) 3.34 ± 2.16 × 1.11 1 (37.87 − 30) 2 + =3.34 ± 0.787 15 1511.3 Question 5: (a) Larger variance of X makes the SE’s of b0 and b1 smaller by the corresponding formulas. (b) If r is positive, Y will increases by rS Y . If r is negative, Y will decrease by rS Y . (c) The intercept is zero because both X and Y have sample means equal zero. The slope is ~ ~ ~ ~ r = 0.6 because X and Y have s.d. equals one. k/ ~c s_ (3.56) 2 × 11 = 0.96 (16.57) 2 × 13 om e. us t.h R2 = 1− gx x/ Question 6: 5 ht tp :// ih (1.5) 2 + (3.56) 2 = 3.863 , 3.863 × 2.2 =8.50. The prediction interval is 75.62 ± 8.5 0 ...
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